14-1 Control Charts for Variation and Mean 707 The values of D4 and D3 are constants computed by quality-control experts, and they are intended to simplify calculations. The upper and lower control limits of D4R and D3R are values that are roughly equivalent to 99.7% confidence interval limits. It is therefore highly unlikely that values from a statistically stable process would fall beyond those limits. If a value does fall beyond the control limits, it’s very likely that the process is not statistically stable. TABLE 14-2 Control Chart Constants n: Number of Observations in Subgroup R Chart x Chart s Chart D3 D4 A2 A3 B3 B4 2 0.000 3.267 1.880 2.659 0.000 3.267 3 0.000 2.574 1.023 1.954 0.000 2.568 4 0.000 2.282 0.729 1.628 0.000 2.266 5 0.000 2.114 0.577 1.427 0.000 2.089 6 0.000 2.004 0.483 1.287 0.030 1.970 7 0.076 1.924 0.419 1.182 0.118 1.882 8 0.136 1.864 0.373 1.099 0.185 1.815 9 0.184 1.816 0.337 1.032 0.239 1.761 10 0.223 1.777 0.308 0.975 0.284 1.716 Source: Adapted from ASTM Manual on the Presentation of Data and Control Chart Analysis, © 1976 ASTM, pp. 134–136. Reprinted with permission of American Society for Testing and Materials. R Chart of Earth Global Temperatures EXAMPLE 3 Construct a control chart for R using the temperatures listed in Table 14-1. Use the samples of size n = 10 for each of the decades. SOLUTION Refer to Table 14-1 in the Chapter Problem on page 701 to see the column of sample ranges R. The value of R is the mean of those 14 sample ranges, so its value is found as follows: R = 0.490 + 0.410 + g+ 1.210 14 = 0.4371 The centerline for our R chart is therefore located at R = 0.4371°C. To find the upper and lower control limits, we must first find the values of D3 and D4. Referring to Table 14-2 for n = 10, we get D4 = 1.777 and D3 = 0.223, so the control limits are as follows: Upper control limit 1UCL2: D4R = 11.777210.43712 = 0.7767 Lower control limit 1LCL2: D3R = 10.223210.43712 = 0.0975 Using a centerline value of R = 0.4371 and control limits of 0.7767 and 0.0975, we now proceed to plot the 14 sample ranges as 14 individual points. The result is shown in the following display. continued Costly Assignable Variation The Mars Climate Orbiter was launched by NASA and sent to Mars, but it was destroyed when it flew too close to Mars. The loss was estimated at $125 million. The cause of the crash was found to be confusion over the units used for calculations. Acceleration data were provided in the English units of pounds of force, but the Jet Propulsion Laboratory assumed that those units were in metric “newtons” instead of pounds. The thrusters of the spacecraft subsequently provided wrong amounts of force in adjusting the position of the spacecraft. The errors caused by the discrepancy were fairly small at first, but the cumulative error over months of the spacecraft’s journey proved to be fatal to its success. In 1962, the rocket carrying the Mariner 1 satellite was destroyed by ground controllers when it went off course due to a missing minus sign in a computer program. CP
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